Metastable states of the random-field Ising chain

Abstract

Using a numerical transfer-matrix method, the authors have determined the number of zero-temperature metastable states and their distribution in energy and magnetization for random-field Ising chains. Both discrete and continuous distributions of the random fields are considered. The degeneracy and structure of the metastable states and ground states for the discrete case may be understood in terms of a domain picture. Algorithms for generating exact ground-state configurations for both discrete and continuous distributions are described, and these demonstrate that the ground states of the random-field Ising chain have a hierarchical structure.